Theorem bicon4d 402

Description: A contraposition deduction.

Hypothesis

Ref	Expression
bicon4d.1	⊢ (φ → (¬ ψ ↔ ¬ χ))

Assertion

Ref	Expression
bicon4d	⊢ (φ → (ψ ↔ χ))

Proof of Theorem bicon4d

Step	Hyp	Ref	Expression
1		bicon4d.1	. 2 ⊢ (φ → (¬ ψ ↔ ¬ χ))
2		pm4.11 400	. 2 ⊢ ((ψ ↔ χ) ↔ (¬ ψ ↔ ¬ χ))
3	1, 2	sylibr 175	1 ⊢ (φ → (ψ ↔ χ))

Syntax hints:  ¬ wn 1   → wi 2   ↔ wb 127

This theorem is referenced by:  pm5.21 502  opelxpex 2445  rankr1a 3521  r1val2 3522  ltaddsubt 4357  lt2sq 4414  sq11 4416  norm-it 5080  chrelat3t 5762

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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